Displaying similar documents to “Extremal problems for conditioned brownian motion and the hyperbolic metric”

Concentration of the Brownian bridge on Cartan-Hadamard manifolds with pinched negative sectional curvature

Marc Arnaudon, Thomas Simon (2005)

Annales de l’institut Fourier

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We study the rate of concentration of a Brownian bridge in time one around the corresponding geodesical segment on a Cartan-Hadamard manifold with pinched negative sectional curvature, when the distance between the two extremities tends to infinity. This improves on previous results by A. Eberle, and one of us . Along the way, we derive a new asymptotic estimate for the logarithmic derivative of the heat kernel on such manifolds, in bounded time and with one...

Limiting behaviors of the Brownian motions on hyperbolic spaces

H. Matsumoto (2010)

Colloquium Mathematicae

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Using explicit representations of the Brownian motions on hyperbolic spaces, we show that their almost sure convergence and the central limit theorems for the radial components as time tends to infinity can be easily obtained. We also give a straightforward strategy to obtain explicit expressions for the limit distributions or Poisson kernels.

Sharp estimates of the Green function of hyperbolic Brownian motion

Kamil Bogus, Tomasz Byczkowski, Jacek Małecki (2015)

Studia Mathematica

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The main objective of the work is to provide sharp two-sided estimates of the λ-Green function, λ ≥ 0, of the hyperbolic Brownian motion of a half-space. We rely on the recent results obtained by K. Bogus and J. Małecki (2015), regarding precise estimates of the Bessel heat kernel for half-lines. We also substantially use the results of H. Matsumoto and M. Yor (2005) on distributions of exponential functionals of Brownian motion.

Exponential functionals of brownian motion and class-one Whittaker functions

Fabrice Baudoin, Neil O’Connell (2011)

Annales de l'I.H.P. Probabilités et statistiques

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We consider exponential functionals of a brownian motion with drift in ℝ, defined via a collection of linear functionals. We give a characterisation of the Laplace transform of their joint law as the unique bounded solution, up to a constant factor, to a Schrödinger-type partial differential equation. We derive a similar equation for the probability density. We then characterise all diffusions which can be interpreted as having the law of the brownian motion with drift conditioned on...